Decentralized Charging Control for Large Populations of Plug-in Electric Vehicles: Application of the Nash Certainty Equivalence Principle

The paper develops a novel decentralized charging control strategy for large populations of plug-in electric vehicles (PEVs). The proposed algorithm is an application of the Nash certainty equivalence principle (or mean-field games). We consider the situation where PEV agents are rational and weakly coupled via their operation costs. At an established Nash equilibrium, each of the PEV agents reacts optimally with respect to the average charging strategy of all the PEV agents. Each of the average charging strategies can be approximated by an infinite population limit which is the solution of a fixed point problem. The control objective is to minimize electricity generation costs by establishing a PEV charging schedule that fills the overnight demand valley. The paper shows that under certain mild conditions, there exists a unique Nash equilibrium that almost satisfies that goal. Moreover, the paper establishes a sufficient condition under which the system converges to the unique Nash equilibrium. The theoretical results are illustrated through various numerical examples.